Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains “rigid” under this process. We show that some positive results can be obtained using ideas of Gabber, Gillet-...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

We introduce the notion of n-fold implicative filters and n-fold implicative lattice implication algebras. We give characterizations of n-fold implicative filters and nfold implicative lattice implication algebras. Finally, we construct an extension property for n-fold implicative filter. 2000 Mathematics Subject Classification. 03G10, 06B10.

In commutative algebra, a Weitzenböck derivation is a nonzero triangular linear derivation of the polynomial algebra K[x1, . . . , xm] in several variables over a field K of characteristic 0. The classical theorem of Weitzenböck states that the algebra of constants is finitely generated. (This algebra coincides with the algebra of invariants of a single unipotent transformation.) In this paper ...

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...

We investigate the behavior of standard bases (in the sense of Hironaka and Grauert) for ideals in rings of formal power series over commutative rings with respect to specializations of the coefficients. For instance, we show that any ideal I of the ring of formal power series A[[X]] = A[[X1, . . . , XN ]] with coefficients in a Noetherian ring A admits a standard basis whose image under every ...

We study the normalization of a monomial ideal and show how to compute its Hilbert function if the ideal is zero dimensional. A positive lower bound for the second coefficient of the Hilbert polynomial is shown. 1 Normalization of monomial ideals In the sequel we use [3, 11] as references for standard terminology and notation on commutative algebra and polyhedral cones. We denote the set of non...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

We introduce non-commutative analogs of k-Schur functions and prove that their images by the noncommutative nabla operator H is ribbon Schur positive, up to a global sign. Inspired by these results, we define new filtrations of the usual (q, t)-Catalan polynomials by computing the image of certain commutative k-Schur functions by the commutative nabla operator∇. In some particular cases, we giv...